Charge-carrier Diffusion and Radia3ve Efficiencies in Hybrid Metal Halide Perovskites Prof Laura Herz Clarendon Laboratory, University of Oxford VIS ? THz I UNSW 2016 The race for efficient, cost-effec7ve photovoltaic cells Multi-junction, crystalline inorganics single-junction, crystalline inorganics (GaAs,Si) CIGS Solution-processed (or low-T evaporated) organics and DSCs http://www.nrel.gov/ncpv/images/efficiency_chart.jpg Hybrid Metal- Halide Perovskites Background: solar cell architectures and materials “Planar heterojuncon” solar cells “Excitonic” or “nanocomposite” cells • Low exciton Binding energy • High exciton Binding energy → mostly free charges at 300K → require energy offsets to induce • High charge-carrier moBility and charge separaon diffusion lengths → doping • Low charge-carrier diffusion lengths gradients or electron/hole- → must separate charges into selec7ve contacts suffice to different material components to collect charges effec7vely inhiBit recomBinaon Organic Photovoltaics (OPV) nm 200 - + - + - + - + Typical examples: crystalline silicon Typical examples: Dye-sensi7zed solar or GaAs solar cells cells (DSC), organic photovoltaics (OPV) Features: highly efficient, But Features: lower efficiencies, cheap energy-intensive fabricaon (low-temperature processing) Charge diffusion in hyBrid lead trihalide perovskites light pulse Excite MA-PBI3-x Clx film on which either electron perovskite (PCBM) or hole (spiro- PL quencher OMeTAD) acceptor has Been deposited Model PL quenching as arising from diffusion of Time after excitation (ns) charge carriers to Extract charge-carrier interface, assuming unity diffusion length L=√(Dτ) quenching efficiency of ≈1μm Stranks, Eperon, Grancini, Menelaou, Alcocer, Leijtens, Herz, Petrozza, Snaith, Science 342, 341 (2013). HyBrid lead trihalide perovskites comBine the Best of Both worlds: low- temperature processing yielding charge carrier diffusion lengths that exceed the op7cal absorp7on depth! Organic-inorganic trihalide perovskite solar cells: HyBrid metal halide perovskites have rapidly established themselves as new optoelectronic materials, allowing: • solar cells with high PCE >20% • varied range of processing protocols • low-cost, abundant ingredients • high absorp7on in the solar range • long (micron) charge diffusion Metal Cathode Metal Cathode HTM Perovskite HTM lengths allow for planar Perovskite Mesoporous TiO2 heterojunc7on designs ETM ETM • light-emission/lasing reported Metal anode Metal anode What are the mechanisms governing charge- carrier moBility, recomBinaon and diffusion? How are optoelectronic proper7es affected By composion? Outline Prototypical MA-PbI3 & MA-PbI3-xClx: Other materials/properes? excellent optoelectronic properes! Lead-free? MA-SnI3 • Propensity towards 7n vacancies gives rise to uninten7onal hole doping • Rapid charge recomBinaon Tuneable materials for tandems? • Shallow, low-density traps A-Pb(BrxI1-x)3 • Non-Langevin Bimolecular recomBinaon • Allows for perovskites with Eg~1.7eV • Strong radiave Bimolecular transi7ons near the ideal Band gap for tandem • Decent charge-carrier moBility and solar cells with silicon long charge diffusion lengths • ProBlems with (photo-)stability • Mostly homogeneous emission Broadening Charge recomBinaon mechanisms in hyBrid lead trihalide perovskites Trap-mediated (k1) Bimolecular (k2) Auger (k3) phonon CB2 CB1 CB1 CB1 CB1 E e- trap k VB1 VB1 VB1 VB1 * non-radiave* radiave , for a direct non-radiave* semiconductor monomolecular strong dependence on hence to some extent Bandstructure, phonons, par7cularly detrimental required to achieve impuri7es (Because of energy & in low-charge-density strong absorp7on momentum conservaon) regime Herz, Ann. Rev. Phys. Chem. 67 (2016) DOI:10.1146/annurev-physchem-040215-112222 *see e.g. Bolink, Adv. Mater. 27, 1837 (2015); Saba, Nat. Commun. 5, 5049 (2014) Charge recomBinaon mechanisms in hyBrid lead trihalide perovskites Trap-mediated (k1) Bimolecular (k2) Auger (k3) phonon CB2 CB1 CB1 CB1 CB1 E e- trap k VB1 VB1 VB1 VB1 Rate equaon governing the recomBinaon dynamics Examine temperature-dependence of each rate constant to understand the different underlying mechanisms, and how each rate can Be tuned! ProBing charge dynamics in hyBrid perovskites read-out pulse pump pulse chopper Woll. Examine transient THz conducvity and sample ZnTe λ/4 prism - photoluminescence (PL) decay dynamics THz following excitaon with VIS light pulse: probe THz read-out through electro-optic sampling delay δ • With increasing pump fluence, the decay MA-PBI3-x Clx dynamics Become increasingly rapid. on quartz • At low fluence, transients Become mono- exponen7al with ~100ns life7me • Can extract k1, k2, k3 from such transients THz photoconductivity through gloBal fits • Can oBtain effec7ve charge-carrier moBility from THz photoconduc7vity Wehrenfennig, Liu, Johnston, Snaith, Herz, Energy Env. Sci. 7, 2269 (2014) J. Phys. Chem. Le. 5, 1300 (2014) Trap-mediated charge recomBinaon in MAPBI3 CB1 Analysis of temperature-dependent PL from solu7on-processed MAPBI3 films, excited with low fluence so that monomolecular decay dominates: trap PL transients: PL peak orthorhomBic tetragonal cuBic and absorp7on onset VB1 energies as a func7on of T: orthorhomBic tetragonal cuBic MAPBI3 ! ! ! • Mono-molecular charge recomBinaon at low fluences in the photoluminescence transient tail • Trap-related charge-carrier recomBinaon Becomes faster at higher temperatures Milot, Eperon, Snaith, Johnston, Herz, Adv. Func. Mater. 25, 6218 (2015) Trap-mediated charge recomBinaon in MAPBI3 + CB1 Increased trap-mediated recombinaon rate with increasing temperature: trap + MAPBI3 ~20meV Ea At high T, ionized, charged VB1 impuri7es may have larger cross-sec7on for charge capture. Ac7vaon energy crystal-phase specific, But mostly shallow traps at room-temperature 14 -3 Relevance to PV opera3on: n<10 cm • leads to decline in charge-carrier diffusion lengths Ld (also Because charge moBility declines with increasing T) MAPBI3 • But: s7ll high Ld~1μm at 70°C. Milot, Eperon, Snaith, Johnston, Herz, Adv. Func. Mater. 25, 6218 (2015) Bi-molecular recomBinaon (k2) in hyBrid lead trihalide perovskites CB1 What are the mechanisms governing Bimolecular recomBinaon in lead-halide perovskites? VB1 One possible model: Langevin theory • Electron moves in electric field generated By hole E J=neμE(r) _ • Capture and recomBinaon occurs at distance r + c r where interac7on energy is comparable to kbT. c r 0 2 • Current into capture radius: I=ne μ/ε0εr must Be kBT equal to rate of change of charge density through capture at: recomBinaon: dQ/dt=nek2 Material MoBility Measured k2/μ k2/μ : e/ε0εr Rao defies evaporated 2 -1 -1 -12 -6 Langevin Φμ=33cm V s k2/μ=3.3×10 cm V 3×10 εr : 1 MA-PBI3-xClx limit By ≈5 2 -1 -1 -6 orders of Anthracene μ=2cm V s k2/μ=6×10 cm V 3.3 : 1 magnitude! Wehrenfennig, Liu, Johnston, Snaith, Herz, Energy Env. Sci. 7, 2269 (2014) Bimolecular charge-recomBinaon in MAPBI3: dependence on temperature T CB1 Photoconducvity dynamics in thin films of MAPbI3 as a func3on of temperature: • Higher-order recomBinaon Becomes more prominent at lower temperature VB1 • Extract Bimolecular recomBinaon rate constant k2 as a func7on of T: MAPBI3 • Expected from Langevin Theory: charge- carrier moBility increases with decreasing T • From Band-structure picture: enhancements in Band-edge transi7ons as thermal ! occupaon of electron-hole states narrows Milot, Eperon, Snaith, Johnston, Herz, Adv. Func. Mater. 25, 6218 (2015) Auger charge-recomBinaon in MAPBI3: dependence on temperature phonon CB2 Auger rate constants (k3) in MAPbI3: • k3 shows expected strong dependence on temperature CB1 CB1 • shows different temperature-dependences in different crystal structures VB1 VB1 • Confirms strong dependence on Bandstructure & phonons • Allows tuning through structure/compositon modificaon Relevance for devices: -28 MAPBI3 • at room temperature: k3~10 cm6s-1 • ~25×higher than that for GaAs (4×10-30cm6s-1) • Auger recomBinaon contriButes significantly for n>>1018cm-3, so not par7cularly relevant for PV, But highly important for lasers. Milot, Eperon, Snaith, Johnston, Herz, Adv. Func. Mater. 25, 6218 (2015) Charge-carrier moBili7es in MAPBI3 Are charge Drude conducvity: mobilies in high-quality lead iodide perovskite films near the intrinsic limit? THz photoconduc7vity spectra are MAPBI Re(σ) 3 σ compaBle with a Drude-response, i.e. only limited By Im(σ) momentum scaering conductivity 0 ω The moBility increases with decreasing T according to T-1.5 in accordance with charge scaering off phonons MAPBI3 è scaering off impuri7es and/or crystal Boundaries can only play a minor role. è At T=300K, μ~30 cm2/(Vs) è Unlikely to see increases By many En. Environ. Sci. 7, 2269 (2014) Adv. Func. Mater. 25, 6218 (2015) orders of magnitude Charge-carrier diffusion in MAPBI3 films Can predict what will happen with charge diffusion if trap density is reduced! Evaluate charge-carrier diffusion length LD in MAPBI3 using: where , and we 2 -10 3 -1 assume μ=30cm /(Vs), k2=10 cm s , -28 6 -1 k3=10 cm s In the limit of ultra-low k1, LD depends strongly on charge density n, approaching: nAM1.5 Meaningful values of LD can only Be oBtained with reference to the charge- Johnston & Herz, Acc. Chem. Res. 49, 146 (2016) carrier density present! Calculang charge-carrier density present in MAPBI3 under solar irradiance Obtain spaally averaged value of the charge-carrier density nAM1.5 present under solar illuminaon, non-charge extrac3ng condions (flat band, near VOC) Step 1: oBtain charge-carrier generaon rate under AM1.5 condi7ons: